I'm sure there's others out there; however, I've only ever heard of Singlestone and Brian at Brian Gavin Diamonds recutting a stone for a non-dealer/retailer. You only have one diamond (presumably). Only a cutter looking at it in person can tell you whether it's a suitable candidate for a recut. The inclusions, the depth or the shape of your stone may make a recut impossible, risky or result in too much weight loss for your taste.
As for whether someone will cut a branded stone for you - I suppose you'll have to talk to the holder of the brand. I suppose you can try to have someone mimick it. I don't know what type of legal protection these companies, including GOG has over the design/cut, but I would assume there are some in place and you don't want to infringe on that. However, I don't think any reputable cutter is going to mimick a branded stone completely.
If you're interested in an AVC but would like to recut your stone, I'd talk to Jon at GOG. Jon has a cutter who does AVC's for him. Although frankly, I don't think Jon will allow you to use his cutter and patented design, but who knows? It's Jon's call. You should phone GOG and speak to him directly.
